**5. Conclusions**

The finite element method (FEM) is the numerical method for solving problems of engineering and mathematical physics, including the calculation of shell structures. Establishing the balance equation describing the vibration of shell structure is quite simple and it is very convenient for coding on a personal computer (PC). The proposed program is able to analyze the static bending, dynamic response, nonlinear problems, etc., with complicated structures, which are not easy to solve by analytical methods.

Based on the finite element method, we established the equilibrium equation of a triple-layer composite shell with shear connectors subjected to dynamic loads. In this paper, employing of the eight-node isometric element is suitable. To exactly describe the strain field, the displacements of the three-layer shell with shear connectors, and the 13-degrees of freedom element is used, in which the three layers have the same a degree of freedom in the *z*-direction, and the other 12 degrees of freedom are described as the linear displacement and rotation angle of each layer. Hence, the displacement field and the strain field of each layer can be investigated deeply. We have created the program in the MATLAB environment to investigate effects of various geometrical parameters on free and forced vibrations of shells. To sum up, some main interesting points of this paper are listed in the following statements.

In general, the geometrical parameters effect strongly on free and forced vibrations of the shell; when the shape of the shell is small, the structure gets stiffer.

Based on the numerical results, we realized that for this type of structure, the shear coefficient of the stub plays a very important role. Especially, when the stiffness of the shear coefficient is large enough, this structure seems to be a sandwich shell.

From the above computed results, we sugges<sup>t</sup> that in order to reduce the vibration of such a structure, we should use the middle layer, having the elastic modulus less than other layers, and the thickness of the middle layer 20–30 times larger than the other ones.

We sugges<sup>t</sup> that, in order to reduce the volume of the shell structure subjected to the blast load, we should consider the triple-layer shell with the core layer having a smaller density than the two layers others. Another interesting thing is that the core layer has less stiffener than the other two layers for the displacement response, the velocity is almost unchanged, so we can be flexible in making shells with available materials and different stiffeners.

Based on the achieved numerical results, this paper also leads to further works; for instance, the analysis of FGM structures with shear connectors, buckling problems, the composite plate with shear connectors subjected to both temperature and mechanical loads, and so on.

**Author Contributions:** Investigation, H.-N.N.; Software, T.N.C., T.T.T.; Visualization, T.V.K.; Writing–original draft, V.-D.P.; Writing–review & editing, D.V.T.

**Funding:** This research was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) gran<sup>t</sup> number 107.02-2018.30.

**Acknowledgments:** DVT gratefully acknowledges the supports of Vietnam National Foundation for Science and Technology Development (NAFOSTED) under gran<sup>t</sup> number 107.02-2018.30.

**Conflicts of Interest:** The authors declare no conflict of interest.
